MS02 - MFBM-1
Cartoon Room 1 (#3145) in The Ohio Union

Recent advances in the mathematics of biochemical reaction networks

Monday, July 17 at 04:00pm

SMB2023 SMB2023 Follow Monday during the "MS02" time block.
Room assignment: Cartoon Room 1 (#3145) in The Ohio Union.
Note: this minisymposia has multiple sessions. The other session is MS01-MFBM-1 (click here).

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Tung Nguyen, Matthew Johnson, Jiaxin Jin


Biochemical reaction networks are well known to be useful in modeling complex systems in biology and chemistry, such as gene regulatory networks and signaling cascades. This mini-symposium will showcase recent advancements in the field of reaction networks with a special focus on the connection between the underlying structure or topology of a reaction network and the possible dynamical behaviors that can emerge from it, including various notions of stability and robustness. The talks will feature applications of reaction networks to microbial interactions, insulin signaling, and synthetic gene circuits. We aim to foster a deeper understanding of the complex interplay between network structure and dynamics, and inspire new avenues of research in the field of mathematical biology.

James Brunner

Los Alamos National Laboratory (Biosciences)
"Inferring microbial interactions with their environment from genomic and metagenomic data"
Microbial communities organize through a complex set of interactions between microbes and their environment, and the resulting metabolic impact on the host ecosystem can be profound. Microbial activity has been shown to impact human health, leading to a myriad of treatments meant to manipulate the resident microbiota of the human gut. Additionally, microbes of plant rhizospheres have a strong influence on plant growth and resilience. Finally, microbial communities impact decomposition in terrestrial ecosystems, influencing the way that carbon is stored in soil and removed from the atmosphere. In order to understand, predict, and influence these processes, genome-scale modeling techniques have been developed to translate genomic data into inferred microbial dynamics. However, these techniques have a strong dependence on unknown parameters and initial community compositions, and are often difficult to analyze qualitatively. With the goal of understanding microbial community metabolic dynamics, we infer the series of interaction networks underlying the resource-mediated community model defined by individual genome-scale models. I will present our tool, MetConSIN, for inferring these networks as well as our current efforts to analyze and simplify the model. Finally, I will discuss our future goals for the prediction of microbial community metabolic impact on their host ecosystem.
Additional authors: Marie E. Kroeger, Los Alamos National Laboratory

Tung Nguyen

Texas A&M University (Department of Mathematics)
"Absolute concentration robustness in multi-site phosphorylation networks with a bifunctional enzyme"
Shinar and Feinberg in 2010 introduced the concept of absolute concentration robustness (ACR) to mean the concentration of a certain species (called ACR species) is invariant across all positive steady states. Biological networks with ACR have been observed experimentally in certain signaling systems in E. coli, and recently have also been proposed as synthetic controllers by Kim and Enciso in 2020. Shinar and Feinberg gave a sufficient condition for the existence of an ACR species; that is the network must have a deficiency of one and there are two non-terminal complexes differing in the ACR species. While the condition is easily checked, many biologically important networks do not have a deficiency of exactly one. In this work, we present a large class of biological networks with arbitrary deficiency and capable of exhibiting ACR. Notably, this class contains multi-site phosphorylation cycles with a ``bifunctional' enzyme. We provide the necessary and sufficient conditions for ACR in such a class of networks, and highlight the essential role of bifunctionality for the existence of ACR.
Additional authors: Badal Joshi, Department of Mathematics, California State University San Marcos

Jiaxin Jin

The Ohio State University (Mathematics)
"Weakly reversible deficiency one realizations of polynomial dynamical systems: an algorithmic perspective"
Given a dynamical system with a polynomial right-hand side, can it be generated by a reaction network that possesses certain properties? This question is important because some network properties may guarantee specific {em dynamical} properties, such as existence or uniqueness of equilibria, persistence, permanence, or global stability. Here we focus on this problem in the context of weakly reversible deficiency one networks. In particular, we describe an algorithm for deciding if a polynomial dynamical system admits a weakly reversible deficiency one realization, and identifying one if it does exist. In addition, we show that weakly reversible deficiency one realizations can be partitioned into mutually exclusive Type I and Type II realizations, where Type I realizations guarantee existence and uniqueness of positive steady states, while Type II realizations are related to stoichiometric generators, and therefore to multistability.
Additional authors: Gheorghe Craciun, Department of Mathematics and Department of Biomolecular Chemistry, University of Wisconsin-Madison; Abhishek Deshpande, Center for Computational Natural Sciences and Bioinformatics, International Institute of Information Technology Hyderabad;

Aidan S. Howells

University of Wisconsin–Madison (Mathematics)
"Stochastic reaction networks within interacting compartments"
Stochastic reaction networks, which are typically modeled as continuous-time Markov chains on $mathbb Z^d_{ge0}$, have proven to be a useful tool for the understanding of processes, chemical and otherwise, in homogeneous environments. There are multiple avenues for generalizing away from the assumption that the environment is homogeneous, with the proper modeling choice dependent upon the context of the problem being considered. One such generalization, introduced by Duso and Zechner in 2020, involves a varying number of interacting compartments, or cells, each of which contains an evolving copy of the stochastic reaction system. The novelty of the model is that these compartments also interact via the merging of two compartments (including their contents), the splitting of one compartment into two, and the appearance and destruction of compartments. We will discuss results pertaining to explosivity, transience, recurrence, and positive recurrence of the model, and explore a number of examples demonstrating some possible non-intuitive behaviors. Based on join work with David F. Anderson
Additional authors: David F. Anderson, University of Wisconsin–Madison

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